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xxTIMURxx [149]
3 years ago
6

What is an equation of the line that is perpendicular to y=−4/5x+3 and passes through the point (4, 12) ?

Mathematics
1 answer:
mylen [45]3 years ago
4 0

Let k:y=m_1x+b_1 and l:y=m_2x+b_2

l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}

We have

y=-\dfrac{4}{5}x+3\to m_1=-\dfrac{4}{5}

Therefore

m_2=-\dfrac{1}{-\frac{4}{5}}=\dfrac{5}{4}

We have the equation of a line:

y=\dfrac{5}{4}x+b

Put the coordinates of the point (4, 12) to the equation of the line:

12=\dfrac{5}{4}(4)+b

12=5+b        <em>subtract 5 from both sides</em>

7=b\to b=7

Answer: \boxed{y=\dfrac{5}{4}x+7}

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